Hi issey_king
The way agencies conduct meetings varies, so the answer (unhelpfully) is "it depends". However, there are various things you can think about and prepare, just in case they are needed.
First and foremost - they want to meet you, that's very positive. Be yourself. Be friendly, polite and not too laid back, but be yourself. Don't try to pretend to have more experience than you have but never apologise for the experiences you do have. If you are talking about something that you have done, explain what you have learned from it: that way you can show that every experience (no matter whether it is high or low profile) is a positive one.
Listen to what they ask you and answer as honestly as you can. Don't try to guess what it is they want you to say and don't try to impress by exaggerating, but be enthusiastic rather than dismissive.
Make sure that you have a short monologue/audition piece prepared
even if they have not asked you for one in advance. Every actor should be able to pull something out of the bag if asked. Most adult acting agencies will not ask you for an audition piece, but it does happen occasionally.
Take an up to date CV and photo (and a showreel if you have one).
Be prepared for some of the "usual" questions. Don't prepare scripted answers, but think about some of the things you could be asked. There's no point in worrying about the possible "unusual" questions, you can't guess what those will be!
You may get none of these, but stock questions include things like:
What have you seen at the theatre/cinema recently?
Who do you admire and why?
Where do you see yourself in 5 years/10years time?
What kind of work do you hope to do?
What is your availability like? How easy will it be for you to attend castings?
Why do you want to be an actor?
You may also get the ghastly:
"Tell me a bit about yourself" or
"What have you been doing recently".
The interview/chat is to see what you are like as a person and to assess how you might come across in a casting. There are not really any right or wrong answers - though some people do show up that they are very naive or starstruck (both things to be avoided if possible!). Try to avoid "acting is my passion". It's the sort of cliche that can tend to set one's teeth on edge - even when it's true. If you can show that you are reasonably clued up about the realities of the profession, they are likely to regard you with more respect and you are likely to find the conversation easier.
Make sure you have a list of questions (either in your head or on paper) about the agency. This is a two-way process. They are assessing you, but
you are also assessing them. Think about all the things you want to know. You can judge a lot about an agency by how prepared they are to answer your questions.
Never sign anything on the spot.
Never hand over any money.
If they are not auditioning you, be prepared for them to say "Tell us when you are in something we can come and see".
If they are not auditioning you (and they haven't already seen you perform), be very wary if they are willing to take you on regardless.
I hope it all goes well for you
